Geometric triangulations and the Teichm\"uller TQFT volume conjecture for twist knots

Fathi Ben Aribi; François Guéritaud; Eiichi Piguet-Nakazawa

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arXiv · 1903.09480

Geometric triangulations and the Teichm\"uller TQFT volume conjecture for twist knots

Fathi Ben Aribi·François Guéritaud·Eiichi Piguet-Nakazawa

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Abstract

We construct a new infinite family of ideal triangulations and H-triangulations for the complements of twist knots, using a method originating from Thurston. These triangulations provide a new upper bound for the Matveev complexity of twist knot complements. We then prove that these ideal triangulations are geometric. The proof uses techniques of Futer and the second author, which consist in studying the volume functional on the polyhedron of angle structures. Finally, we use these triangulations to compute explicitly the partition function of the Teichm\"uller TQFT and to prove the associated volume conjecture for all twist knots, using the saddle point method.

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Fathi Ben Aribi, François Guéritaud, Eiichi Piguet-Nakazawa. 2019-03-22. Geometric triangulations and the Teichm\"uller TQFT volume conjecture for twist knots. https://arxiv.org/abs/1903.09480

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